EE281-Electric Circuits

class: center, middle

# EE-281
# Capacitors - Inductors

## Ozan Keysan

[ozan.keysan.me](http://ozan.keysan.me)

Office: C-113 <span class="meta">•</span> Tel: 210 7586

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# Capacitors

![](http://www.mds975.co.uk/Images/radios/capacitors01.jpg)

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#Capacitors

### A capacitor is a device that consists of two conducting plates seperated by an insulator layer.

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# Capacitance

## Capacitance is the ratio of electric charge to voltage.

# \\(C = \dfrac{Q}{V}\\)
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# Capacitance

## can be defined using the material properties.

# \\(C = \dfrac{\varepsilon A}{d}\\)
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## \\(\varepsilon\\): permitivity of the dielectric material
## \\(A\\) is the surface area
## \\(d\\) is the distance between layers.

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# Capacitor Voltage & Current

# \\(i = C\dfrac{dV}{dt}\\)
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# \\(V = \dfrac{1}{C} \int_0^t i(t) dt\\)

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# Energy stored in a capacitor is:

# \\(w = \dfrac{1}{2} C V^2\\)

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# DC Response

# \\(i = C\frac{dV}{dt}\\)
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- ## Current of capacitor is zero if there's no change in the voltage (i.e. DC voltage)
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- ## Capacitor voltage cannot be change instantenously as this means infinite current.

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## Parallel Capacitors

![](https://raw.githubusercontent.com/ozank/ee281/master/images/parallel_capacitor.png)
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## \\(C_{eq} = C_1 + C_2 + C_3 ... + C_N\\)
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# Series Capacitors
![](https://raw.githubusercontent.com/ozank/ee281/master/images/series_capacitors.png)
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## \\(\frac{1}{C\_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} ... \frac{1}{C_N}\\)

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# Series Capacitors
![](https://raw.githubusercontent.com/ozank/ee281/master/images/series_capacitors.png)

### For two capacitors
## \\(C_{eq} = \frac{C_1 C_2}{C_1 + C_2}\\)
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#Exercise
### What is the equivalent capacitance?

![](https://raw.githubusercontent.com/ozank/ee281/master/images/Ceq_ex.png)
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#Exercise
### Find the energy stored in the capacitors?

![](https://raw.githubusercontent.com/ozank/ee281/master/images/Cdc_ex.png)

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# Inductors
![](http://www.coilws.com/images/Inductors%20Group.jpg)

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# Inductance
# \\(L = \dfrac{N^2 \mu A}{l}\\)

### \\(N\\) is the number of turns, \\(\mu\\) is the permeability of the core, \\(A\\) is the cross-section area, \\(l\\) is the mean length of the magnetic flux.
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# Inductors

# \\(V = L \dfrac{di}{dt}\\)
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## \\(I = \dfrac{1}{L} \int_0^t V(t) dt\\)

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## Energy stored in an inductor is:

# \\(w = \dfrac{1}{2} L I^2\\)

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#DC Response
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## - An inductor behaves like short-circuit under DC
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## - Inductor current cannot be change instantenously as this means infinite voltage.

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# Series Connection

Equivalent inductance of series connected inductors are the sum of inductances:

![](https://raw.githubusercontent.com/ozank/ee281/master/images/series_inductors.png)

## \\(L_{eq} = L_1 + L_2 + L_3 ... + L_N\\)

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# Parallel Connection

![](https://raw.githubusercontent.com/ozank/ee281/master/images/parallel_inductor.png)

## \\(\frac{1}{L\_{eq}} = \frac{1}{L_1} + \frac{1}{L_2} + \frac{1}{L_3} ... \frac{1}{L_N}\\)

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# Exercise:
##Find the energy stored in capacitor and inductor under DC conditions.

![](https://raw.githubusercontent.com/ozank/ee281/master/images/Ldc_ex.png)

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# Any questions?

## You can download this presentation from: [keysan.me/ee281](http://keysan.me/ee281)